/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.jar # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty termination of the given Bare JBC problem could be proven: (0) Bare JBC problem (1) BareJBCToJBCProof [EQUIVALENT, 97 ms] (2) JBC problem (3) JBCToGraph [EQUIVALENT, 429 ms] (4) JBCTerminationGraph (5) TerminationGraphToSCCProof [SOUND, 0 ms] (6) JBCTerminationSCC (7) SCCToIRSProof [SOUND, 86 ms] (8) IRSwT (9) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 29 ms] (12) IRSwT (13) IntTRSCompressionProof [EQUIVALENT, 0 ms] (14) IRSwT (15) FilterProof [EQUIVALENT, 0 ms] (16) IntTRS (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IntTRS (19) PolynomialOrderProcessor [EQUIVALENT, 12 ms] (20) YES ---------------------------------------- (0) Obligation: need to prove termination of the following program: public class LogBuiltIn{ public static int log(int x) { int res = 0; while (x > 1) { x = x/2; res++; } return res; } public static void main(String[] args) { Random.args = args; int x = Random.random(); log(x); } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (1) BareJBCToJBCProof (EQUIVALENT) initialized classpath ---------------------------------------- (2) Obligation: need to prove termination of the following program: public class LogBuiltIn{ public static int log(int x) { int res = 0; while (x > 1) { x = x/2; res++; } return res; } public static void main(String[] args) { Random.args = args; int x = Random.random(); log(x); } } public class Random { static String[] args; static int index = 0; public static int random() { String string = args[index]; index++; return string.length(); } } ---------------------------------------- (3) JBCToGraph (EQUIVALENT) Constructed TerminationGraph. ---------------------------------------- (4) Obligation: Termination Graph based on JBC Program: LogBuiltIn.main([Ljava/lang/String;)V: Graph of 121 nodes with 1 SCC. ---------------------------------------- (5) TerminationGraphToSCCProof (SOUND) Splitted TerminationGraph to 1 SCCs. ---------------------------------------- (6) Obligation: SCC of termination graph based on JBC Program. SCC contains nodes from the following methods: LogBuiltIn.main([Ljava/lang/String;)V SCC calls the following helper methods: Performed SCC analyses: *Used field analysis yielded the following read fields: *Marker field analysis yielded the following relations that could be markers: ---------------------------------------- (7) SCCToIRSProof (SOUND) Transformed FIGraph SCCs to intTRSs. Log: Generated rules. Obtained 11 IRulesP rules: f420_0_log_ConstantStackPush(EOS(STATIC_420), i66, i66) -> f422_0_log_LE(EOS(STATIC_422), i66, i66, 1) :|: TRUE f422_0_log_LE(EOS(STATIC_422), i73, i73, matching1) -> f428_0_log_LE(EOS(STATIC_428), i73, i73, 1) :|: TRUE && matching1 = 1 f428_0_log_LE(EOS(STATIC_428), i73, i73, matching1) -> f441_0_log_Load(EOS(STATIC_441), i73) :|: i73 > 1 && matching1 = 1 f441_0_log_Load(EOS(STATIC_441), i73) -> f443_0_log_ConstantStackPush(EOS(STATIC_443), i73) :|: TRUE f443_0_log_ConstantStackPush(EOS(STATIC_443), i73) -> f446_0_log_IntArithmetic(EOS(STATIC_446), i73, 2) :|: TRUE f446_0_log_IntArithmetic(EOS(STATIC_446), i73, matching1) -> f448_0_log_Store(EOS(STATIC_448), i76) :|: i76 = i73 / 2 && i73 > 1 && i76 < i73 && matching1 = 2 f448_0_log_Store(EOS(STATIC_448), i76) -> f451_0_log_Inc(EOS(STATIC_451), i76) :|: TRUE f451_0_log_Inc(EOS(STATIC_451), i76) -> f454_0_log_JMP(EOS(STATIC_454), i76) :|: TRUE f454_0_log_JMP(EOS(STATIC_454), i76) -> f474_0_log_Load(EOS(STATIC_474), i76) :|: TRUE f474_0_log_Load(EOS(STATIC_474), i76) -> f419_0_log_Load(EOS(STATIC_419), i76) :|: TRUE f419_0_log_Load(EOS(STATIC_419), i66) -> f420_0_log_ConstantStackPush(EOS(STATIC_420), i66, i66) :|: TRUE Combined rules. Obtained 2 IRulesP rules: f420_0_log_ConstantStackPush(EOS(STATIC_420), i66:0, i66:0) -> f420_0_log_ConstantStackPush'(EOS(STATIC_420), i66:0, i66:0) :|: i66:0 > 1 && i66:0 > div f420_0_log_ConstantStackPush'(EOS(STATIC_420), i66:0, i66:0) -> f420_0_log_ConstantStackPush(EOS(STATIC_420), div, div) :|: i66:0 > 1 && i66:0 > div && i66:0 - 2 * div < 2 && i66:0 - 2 * div > -2 Filtered constant ground arguments: f420_0_log_ConstantStackPush(x1, x2, x3) -> f420_0_log_ConstantStackPush(x2, x3) f420_0_log_ConstantStackPush'(x1, x2, x3) -> f420_0_log_ConstantStackPush'(x2, x3) EOS(x1) -> EOS Filtered duplicate arguments: f420_0_log_ConstantStackPush(x1, x2) -> f420_0_log_ConstantStackPush(x2) f420_0_log_ConstantStackPush'(x1, x2) -> f420_0_log_ConstantStackPush'(x2) Finished conversion. Obtained 2 rules.P rules: f420_0_log_ConstantStackPush(i66:0) -> f420_0_log_ConstantStackPush'(i66:0) :|: i66:0 > 1 && i66:0 > div f420_0_log_ConstantStackPush'(i66:0) -> f420_0_log_ConstantStackPush(div) :|: i66:0 > div && i66:0 > 1 && i66:0 - 2 * div > -2 && i66:0 - 2 * div < 2 ---------------------------------------- (8) Obligation: Rules: f420_0_log_ConstantStackPush(x) -> f420_0_log_ConstantStackPush'(x) :|: x > 1 && x > x1 f420_0_log_ConstantStackPush'(x2) -> f420_0_log_ConstantStackPush(x3) :|: x2 > x3 && x2 > 1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 ---------------------------------------- (9) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (10) Obligation: Rules: f420_0_log_ConstantStackPush(x) -> f420_0_log_ConstantStackPush'(x) :|: x > 1 && x > x1 f420_0_log_ConstantStackPush'(x2) -> f420_0_log_ConstantStackPush(x3) :|: x2 > x3 && x2 > 1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f420_0_log_ConstantStackPush(x) -> f420_0_log_ConstantStackPush'(x) :|: x > 1 && x > x1 (2) f420_0_log_ConstantStackPush'(x2) -> f420_0_log_ConstantStackPush(x3) :|: x2 > x3 && x2 > 1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (12) Obligation: Termination digraph: Nodes: (1) f420_0_log_ConstantStackPush(x) -> f420_0_log_ConstantStackPush'(x) :|: x > 1 && x > x1 (2) f420_0_log_ConstantStackPush'(x2) -> f420_0_log_ConstantStackPush(x3) :|: x2 > x3 && x2 > 1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2 Arcs: (1) -> (2) (2) -> (1) This digraph is fully evaluated! ---------------------------------------- (13) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (14) Obligation: Rules: f420_0_log_ConstantStackPush(x:0) -> f420_0_log_ConstantStackPush(x3:0) :|: x:0 > x1:0 && x:0 - 2 * x3:0 < 2 && x:0 - 2 * x3:0 > -2 && x:0 > 1 && x:0 > x3:0 ---------------------------------------- (15) FilterProof (EQUIVALENT) Used the following sort dictionary for filtering: f420_0_log_ConstantStackPush(INTEGER) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f420_0_log_ConstantStackPush(x:0) -> f420_0_log_ConstantStackPush(x3:0) :|: x:0 > x1:0 && x:0 - 2 * x3:0 < 2 && x:0 - 2 * x3:0 > -2 && x:0 > 1 && x:0 > x3:0 ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: f420_0_log_ConstantStackPush(x:0:0) -> f420_0_log_ConstantStackPush(x3:0:0) :|: x:0:0 > 1 && x:0:0 > x3:0:0 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 - 2 * x3:0:0 < 2 && x:0:0 > x1:0:0 ---------------------------------------- (19) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f420_0_log_ConstantStackPush(x)] = x The following rules are decreasing: f420_0_log_ConstantStackPush(x:0:0) -> f420_0_log_ConstantStackPush(x3:0:0) :|: x:0:0 > 1 && x:0:0 > x3:0:0 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 - 2 * x3:0:0 < 2 && x:0:0 > x1:0:0 The following rules are bounded: f420_0_log_ConstantStackPush(x:0:0) -> f420_0_log_ConstantStackPush(x3:0:0) :|: x:0:0 > 1 && x:0:0 > x3:0:0 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 - 2 * x3:0:0 < 2 && x:0:0 > x1:0:0 ---------------------------------------- (20) YES